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"... Abstract. There are many powerful techniques for automated termination analysis of term rewriting. However, up to now they have hardly been used for real programming languages. We present a new approach which permits the application of existing techniques from term rewriting in order to prove termin ..."

Abstract. There are many powerful techniques for automated termination analysis of term rewriting. However, up to now they have hardly been used for real programming languages. We present a new approach which permits the application of existing techniques from term rewriting in order to prove termination of programs in the functional language Haskell. In particular, we show how termination techniques for ordinary rewriting can be used to handle those features of Haskell which are missing in term rewriting (e.g., lazy evaluation, polymorphic types, and higherorder functions). We implemented our results in the termination prover AProVE and successfully evaluated them on existing Haskell-libraries. 1

The paradigm of type-based termination is explored for functional programming with recursive data types. The article introduces , a lambda-calculus with recursion, inductive types, subtyping and bounded quanti cation. Decorated type variables representing approximations of inductive types are used to track the size of function arguments and return values. The system is shown to be type safe and strongly normalizing. The main novelty is a bidirectional type checking algorithm whose soundness is established formally.

"... We now define the notion, already discussed, of an effectively calculable function of positive integers by identifying it with the notion of a recursive function of positive integers (or of a lambdadefinable function of positive integers). The phrase in parentheses refers to the apparatus which Chur ..."

We now define the notion, already discussed, of an effectively calculable function of positive integers by identifying it with the notion of a recursive function of positive integers (or of a lambdadefinable function of positive integers). The phrase in parentheses refers to the apparatus which Church had developed to investigate this and other problems in the foundations of mathematics: the calculus of lambda conversion. Both the Thesis and the lambda calculus have been of seminal influence on the development of Computing Science. The main subject of this article is the lambda calculus but I will begin with a brief sketch of the emergence of the Thesis. The epistemological status of Church’s Thesis is not immediately clear from the above quotation and remains a matter of debate, as is explored in other papers of this volume. My own view, which I will state but not elaborate here, is that the thesis is empirical because it relies for its significance on a claim about what can be calculated by mechanisms. This becomes clearer in

"... A type theoretic programming language is introduced that is based on lambda calculus with coproducts, products and inductive types, and additionally allows the definition of recursive functions in the way that is common in most functional programming languages. A formal system is presented that chec ..."

A type theoretic programming language is introduced that is based on lambda calculus with coproducts, products and inductive types, and additionally allows the definition of recursive functions in the way that is common in most functional programming languages. A formal system is presented that checks whether such a definition is structurally recursive and a soundness theorem is shown for this system. Thus all functions passing this check are ensured to terminate on all inputs. For the moment only non-mutual recursive functions are considered. 1

Distributed Fault Tolerance entails detecting errors, confining the damage caused, recovery from the errors, and providing continued service on a network of co-operating machines. Functional languages potentially offer benefits for distributed fault tolerance: many computations are pure, and hence have no side-effects to be reversed during error recovery. Moreover functional languages have a high-level runtime system (RTS) where computations and data are readily manipulated. We propose a new RTS level of fault tolerance for distributed functional languages, and outline a design for its implementation for the GdH language. Glasgow distributed Haskell is a small extension to the Haskell language and the fault tolerance design utilises existing distributed graph reduction mechanisms. The design distinguishes between pure and impure computations; impure or side effecting computations must be recovered using conventional exceptionbased techniques, but the RTS attempts implicit backward recovery of pure computations.

"... Functional languages potentially oer benefits for distributed fault tolerance: many computations are pure, and hence have no side-effects to be reversed during error recovery; moreover functional languages have a high-level runtime system (RTS) where computations and data are readily manipulated. ..."

Functional languages potentially oer benefits for distributed fault tolerance: many computations are pure, and hence have no side-effects to be reversed during error recovery; moreover functional languages have a high-level runtime system (RTS) where computations and data are readily manipulated. We propose a new RTS level of fault tolerance for distributed functional languages, and outline a design for its implementation for the GdH language. The design distinguishes between pure and impure computations: impure computations must be recovered using conventional exception-based techniques, but the RTS attempts implicit recovery of pure computations.

"... There are many powerful techniques for automated termination analysis of term rewriting. However, up to now they have hardly been used for real programming languages. We present a new approach which permits the application of existing techniques from term rewriting to prove termination of most funct ..."

There are many powerful techniques for automated termination analysis of term rewriting. However, up to now they have hardly been used for real programming languages. We present a new approach which permits the application of existing techniques from term rewriting to prove termination of most functions defined in Haskell programs. In particular, we show how termination techniques for ordinary rewriting can be used to handle those features of Haskell which are missing in term rewriting (e.g., lazy evaluation, polymorphic types, and higher-order functions). We implemented our results in the termination prover AProVE and successfully evaluated them on existing Haskell-libraries.

"... Abstract: The driving idea of functional programming is to make programming more closely related to mathematics. A program in a functional language such as Haskell or Miranda consists of equations which are both computation rules and a basis for simple algebraic reasoning about the functions and dat ..."

Abstract: The driving idea of functional programming is to make programming more closely related to mathematics. A program in a functional language such as Haskell or Miranda consists of equations which are both computation rules and a basis for simple algebraic reasoning about the functions and data structures they define. The existing model of functional programming, although elegant and powerful, is compromised to a greater extent than is commonly recognised by the presence of partial functions. We consider a simple discipline of total functional programming designed to exclude the possibility of non-termination. Among other things this requires a type distinction between data, which is finite, and codata, which is potentially infinite. Key Words: functional programming Category: D.1.1

"... Abstract: The driving idea of functional programming is to make programming more closely related to mathematics. A program in a functional language such as Haskell or Miranda consists of equations which are both computation rules and a basis for simple algebraic reasoning about the functions and dat ..."

Abstract: The driving idea of functional programming is to make programming more closely related to mathematics. A program in a functional language such as Haskell or Miranda consists of equations which are both computation rules and a basis for simple algebraic reasoning about the functions and data structures they define. The existing model of functional programming, although elegant and powerful, is compromised to a greater extent than is commonly recognised by the presence of partial functions. We consider a simple discipline of total functional programming designed to exclude the possibility of non-termination. Among other things this requires a type distinction between data, which is finite, and codata, which is potentially infinite. Key Words: functional programming Category: D.1.1

"... This work presents an automatic cost-analysis system for an implicitly parallel skeletal programming language. Although deducing interesting dynamic characteristics of parallel programs (and in particular, run time) is well known to be an intractable problem in the general case, it can be alleviated ..."

This work presents an automatic cost-analysis system for an implicitly parallel skeletal programming language. Although deducing interesting dynamic characteristics of parallel programs (and in particular, run time) is well known to be an intractable problem in the general case, it can be alleviated by placing restrictions upon the programs which can be expressed. By combining two research threads, the “skeletal ” and “shapely ” paradigms which take this route, we produce a completely automated, computation and communication sensitive cost analysis system. This builds on earlier work in the area by quantifying communication as well as computation costs, with the former being derived for the Bulk Synchronous Parallel (BSP) model. We present details of our shapely skeletal language and its BSP implementation strat-egy together with an account of the analysis mechanism by which program behaviour information (such as shape and cost) is statically deduced. This information can be used at compile-time to optimise a BSP implementation and to analyse computation and communication costs. The analysis has been implemented in Haskell. We con-sider different algorithms expressed in our language for some example problems and illustrate each BSP implementation, contrasting the analysis of their efficiency by tra-ditional, intuitive methods with that achieved by our cost calculator. The accuracy of cost predictions by our cost calculator against the run time of real parallel programs is tested experimentally. Previous shape-based cost analysis required all elements of a vector (our nestable bulk data structure) to have the same shape. We partially relax this strict requirement on data structure regularity by introducing new shape expressions in our analysis framework. We demonstrate that this allows us to achieve the first automated analysis of a complete derivation, the well known maximum segment sum algorithm of Skillicorn and Cai. 3 4